code: def supports_cache_root(model: Model) -> bool:
      r"""Checks if a model supports the cache_root functionality.
      The two criteria are that the model is not multi-task and the model
      produces a GPyTorchPosterior.
      """
      if isinstance(model, ModelListGP):
          return all(supports_cache_root(m) for m in model.models)
      # Multi task models and non-GPyTorch models are not supported.
      if isinstance(
          model, (MultiTaskGP, KroneckerMultiTaskGP, HigherOrderGP)
      ) or not isinstance(model, GPyTorchModel):
          return False
      # Models that return a TransformedPosterior are not supported.
      if hasattr(model, "outcome_transform") and (
          not model.outcome_transform._is_linear
      ):
          return False
      return True
  
imports: from __future__ import annotations
  import warnings
  from typing import Optional
  import torch
  from botorch.acquisition.acquisition import MCSamplerMixin
  from botorch.exceptions.warnings import BotorchWarning
  from botorch.models.gpytorch import GPyTorchModel
  from botorch.models.higher_order_gp import HigherOrderGP
  from botorch.models.model import Model
  from botorch.models.model_list_gp_regression import ModelListGP
  from botorch.models.multitask import KroneckerMultiTaskGP, MultiTaskGP
  from botorch.posteriors.gpytorch import GPyTorchPosterior
  from botorch.posteriors.posterior import Posterior
  from botorch.sampling.base import MCSampler
  from botorch.utils.low_rank import extract_batch_covar, sample_cached_cholesky
  from gpytorch.distributions.multitask_multivariate_normal import MultitaskMultivariateNormal
  from linear_operator.utils.errors import NanError, NotPSDError
  from torch import Tensor
label_desc: Use image node_id 1 for calling a global function with example usage: supports_cache_root(model) and returns: True, all, False, False